Journal of Computational and Applied Mathematics
Nonlinear dynamical systems, which include models of the Earth's climate, financial markets and complex ecosystems, often undergo abrupt transitions that lead to radically different behavior. The ability to predict such qualitative and potentially disruptive changes is an important problem with far-reaching implications. Even with robust mathematical models, predicting such critical transitions prior to their occurrence is extremely difficult. In this work, we propose a machine learning method to study the parameter space of a complex system, where the dynamics is coarsely characterized using topological invariants. We show that by using a nearest neighbor algorithm to sample the parameter space in a specific manner, we are able to predict with high accuracy the locations of critical transitions in parameter space. (C) 2011 Elsevier B.V. All rights reserved.
Berwald, J., Gedeon, T., & Sheppard, J. (2012). Using machine learning to predict catastrophes in dynamical systems. Journal of Computational and Applied Mathematics, 236(9), 2235-2245.